Question

Solve: $(3x-5{)}^2+(3x+5{)}^2$ = $(18x+10)(x-2)$

• A. $\frac{-35}{13}$
• B. $\frac{-25}{13}$
• C. $\frac{-15}{13}$
• D. $\frac{-45}{13}$

Answer 1

The correct option is A $\frac{-35}{13}$

We will solve the given expression $(3x-5{)}^2+(3x+5{)}^2=(18x+10)(x-2)$ as shown below:

$(3x-5{)}^2+(3x+5{)}^2=(18x+10)(x-2)\Rightarrow \left[\right(3x{)}^2+(5{)}^2-(2\times 3x\times 5\left)\right]+\left[\right(3x{)}^2+(5{)}^2+(2\times 3x\times 5\left)\right]=18x(x-2)+10(x-2)(\because (a+b{)}^2=a^2+b^2+2ab,(a-b{)}^2=a^2+b^2-2ab)\Rightarrow 9x^2+25-30x+9x^2+25+30x=18x^2-36x+10x-20\Rightarrow 18x^2+50=18x^2-26x-20\Rightarrow 18x^2+50-18x^2+26x+20=0$

$\Rightarrow 26x+70=0\Rightarrow 26x=-70\Rightarrow x=-\frac{70}{26}\Rightarrow x=-\frac{35}{13}$

Hence, $x=-\frac{35}{13}$.